We address the representation of binary images using mathematical morphology. One of the main image representations in binary mathematical morphology is the shape decomposition representation, useful for image compression, pattern recognition, and image interpolation. The binary Morphological shape decomposition (MSD) representation can be developed and generalized. With these generalizations, the binary MSD's role as an efficient image decomposition tool is extended. Initially the MSD representation is based on only "one-parameter" families of elements. A new branch is added by introducing a multistructuring element MSD based on the decomposition of images into "multiparameter" families of elements. The MSD representation contains redundant points. Examples are presented and illustrated by computer simulations.